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The results from a survey about the number of siblings a group of people have are shown in the table below.

What is the median number of siblings?

\begin{tabular}{|c|c|}
\hline Number of siblings & Frequency \\
\hline 0 & 9 \\
\hline 1 & 5 \\
\hline 2 & 7 \\
\hline 3 & 1 \\
\hline 4 & 3 \\
\hline
\end{tabular}


Sagot :

To determine the median number of siblings from the given survey data, let's follow these steps:

1. Create a List of All Data Points:
First, we need to list out each data point according to its frequency. Here’s the given table:

[tex]\[ \begin{array}{|c|c|} \hline \text{Number of siblings} & \text{Frequency} \\ \hline 0 & 9 \\ \hline 1 & 5 \\ \hline 2 & 7 \\ \hline 3 & 1 \\ \hline 4 & 3 \\ \hline \end{array} \][/tex]

Based on this table, we create a list with the number of siblings appearing according to their frequencies:

[tex]\[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4] \][/tex]

2. Order the List:
The list is already ordered, but to ensure clarity, here it is again:

[tex]\[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4] \][/tex]

3. Find the Median:
To find the median, we need to determine the middle value in this list. If the number of observations (n) is odd, the median is the middle number. If n is even, the median is the average of the two middle numbers.

- Count the total number of data points: [tex]\( n = 25 \)[/tex].

Since [tex]\( n = 25 \)[/tex], an odd number, the median is the middle value. The middle value is located at position:

[tex]\[ \frac{n + 1}{2} = \frac{25 + 1}{2} = 13 \][/tex]

So, the 13th value in the ordered list is the median. If we count the values:

[tex]\[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, \mathbf{1}, 1, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4] \][/tex]

The 13th value is 1.

Therefore, the median number of siblings is 1.